(a) Consider a ray of light travelling from a denser medium (glass) to a less dense medium (air) at a small angle of incidence.
(i)


As angle of incidence increases i, the angle of refraction r also increases, at a point when r = 90°, i = C (the critical angle)

If the angle of incidence i is made greater than the critical angle C no refraction in the less dense medium, the ray is totally internally reflected.

(b)

An astronomical telescope consists of two converging lenses i.e an objective lens of long focal length fo and an eye piece of short focal length fe. In normal adjustment the principal foci of the lenses coincide, the separation of the lenses d = fo + fe.

(c)(i) But M = \(\frac{v}{u} = 2 = \frac{v}{u}\)
v = 2u
u + v = 90
u + 2u = 90
u = 30cm
f = \(\frac{uv}{u + v} = \frac{u \times 2u}{u + 2u} = \frac{2u}{3}\)
= \(\frac{2 \times 30}{3}\) = 20cm

(iii) U = 2f = 2 x 20
= 40cm